1905-6.] The Y-line Minors of the Square of a Determinant. 539 
the use of single-line arrays as elements all difficulty vanishes, the 
identities then becoming 
a Y + a 2 + ... + a n (a x , a 2 , • . • , a n ) 
(a lt a 2i . . . , a n ) \ + b 2 + ... +b n 
a 1 + a 2 + ... + a n (a 1 , a 2 , . . . , a n ) (a 1 , a 2 , . . . , a n ) 
(Pit b 2 , . . . , b n ) b-^ b 2 -\- ... + b n , b 2 , . . . , b n ) 
i5 ^2 5***5 C n ) (^i j ^2 ’ ' ’ • > ^1 "•* ^2 d" ••• d" C n 
= 2 
I «A C 3 I » 
and so on. 
(. Issued separately January 16 , 1907 .) 
